Power jigsaws with blades that execute reciprocating motions are known, particularly in the form of hand-guided power jigsaws. In them, the lateral guidance and support of the saw blade during the sawing process is largely responsible for the quality of the cut since as it reciprocates in the cut, the saw blade tends to swerve, in particular laterally, away from the resistance presented to it by the material being cut. Viewed in the cutting direction, a lateral deviation of the saw blade from the desired orientation, with the saw blade end moving laterally to the left or right essentially at right angles to the surface of the material being cut, is disadvantageous for the cut quality and saw performance. The mechanical strain due to the bending that this unwanted swerving causes also reduces the service life of the saw blade. The prior art has therefore disclosed pendulum guide devices for such saw blades that execute reciprocating motions. These devices are intended to minimize the free travel distances within which the saw blade is able to deviate during the reciprocating motion. There are conventional embodiments in which the saw blade of power jigsaws is guided by means of a notch in a guide roller or support roller situated between the material being cut and the clamping device in which the saw blade is secured and/or a lateral guidance is provided for the saw blade. There are also known embodiments that provide this lateral guidance additionally or alternatively by means of separate lateral guide jaws in the region directly above the material being cut. In these embodiments, it is disadvantageous that the known saw blade guides do not sufficiently prevent the saw blade from swerving during the reciprocating motion. In these cases, the saw blade itself is deformed in an arc-shaped fashion around the guide element, particularly if only one guide roller is provided between the clamping device and the material being cut, with the one guide element acting as a nodal point with regard to the formation of the arc shape. Particularly in saw blades that execute oscillating motions, this does not assure sufficient guidance of the saw blade in all phases of the oscillating/reciprocating motion. Moreover, the introduction of the oscillating motion into the support element induces considerable strain on the support element and on the spine of the saw blade.